Double-click the side button on the right side of your iPhone. Look at your iPhone to authenticate with Face ID (or place your finger on the Touch ID sensor if it's an older model). Tap the top of your phone to the card reader, usually near where you see a tap-to-pay logo. You'll see a checkmark and hear a ding when the payment reads successfully.
If it doesn't work, ensure the location accepts Apple Pay and that their systems are running. If so, ask someone working there about the best spot to tap on their payment terminal.
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